LiamG... no one seems to have had this problem. I heard one on the Forum where the handle broke and they must have managed to get the door open.
When I have a problem that cannot be figured out, I remove all the hardware I can get out. Eventually you will be down to the part that is holding the door from opening.
You already have a problem. Taking it apart without knowing what you are doing is how you will learn... and you can then tell us.
The hinges... oh... I would not try that. You could be getting into a second repair job IF a hinge casting breaks.
It may be a simple issue of having someone lifting the bottom of the door UP and piddling with whatever seems to be the problem... If you do not know what the problem is... do not avoid the simple options.
Check with replacement parts sales people who may have one of these around. You may be needing one sooner, than later.
I learned how to repair antique Mills Slot Machines by... taking my first one apart that was not working. Made a total mess of it and had no idea what I was doing. After figuring it out, eventually, I can listen on a telephone the sounds being made and explain to the owner what their problem probably would be. So far with 100% success.
Just drill out the rivets holding some parts and buy the tool that fits any odd head. You have nothing to loose... other than your sanity and up to this point you will at least be making progress.
If you can fix this... I will send any slot machine service work your way.